1. Field of the Invention
The invention relates to a method and a device for processing signals of a digital transmission system in general, and for estimating the frequency offset of the transmission system in particular.
2. Description of the Related Art
Digital transmission techniques by means of electromagnetic signals are of particular interest within the context of a continuously growing need for communication and mobility. The rapidly expanding field of mobile radio represents an important application of such digital transmission techniques. In the case of systems for digital transmission, the transmission is typically performed by modulating a carrier frequency such as, for example, in the case of mobile radio in the global system for mobile communications standard (GSM) or in the enhanced data rates for GSM evolution standard (EDGE), which is based thereon.
In the case of carrier-frequency based digital transmission over dispersive channels, for example over a mobile radio channel, unavoidable deviations occur with real systems between the actual carrier frequency of the received signal and the carrier frequency active in the receiver. Causes for the frequency shifts are, for example, tolerances in the frequency standards, that is to say the local oscillators of the transmitter or the receiver, or frequency shifts owing to local movement of the transmitter or receiver, for example by the so-called Doppler effect. The Doppler effect can be modelled starting from a simple shift in the transmitted frequency (Doppler shift) up to a superimposition of infinitely many, infinitely small received signal components with different frequency shifts (Doppler widening). A frequency offset disadvantageously worsens the efficiency of the receiver with respect to the recovery of the transmitted data sequence. This is likewise disadvantageously expressed in a rise in the bit or block error rate. The frequency offset between the instantaneous carrier frequency of the received signal and the carrier frequency of a coherent receiver can be estimated using known methods given specific assumptions. Once the frequency offset is known, measures may be taken in the receiver which permit compensation of an existing frequency offset, and thus improve the efficiency of the receiver with respect to the recovery of the transmitted data.
An overview of known estimation methods is given, for example, in Mengali, U., D'Andrea, A. N. “Synchronization Techniques for Digital Receivers”, Plenum Press, New York, 1997. A theoretically efficient method is known under the designation of “Data Aided Maximum Likelihood Frequency Estimation”. However, the said method requires a two-step search algorithm, and is therefore exceptionally laborious computationally. For this reason, the method is unsuitable for practical use.
Also known are already simplified variants of the quoted method which are likewise based on data-aided estimation of the frequency offset. Some of these methods are described, for example, in S. Kay, “A Fast and Accurate Single Frequency Estimator”, IEEE Trans. Acoust. Speech, Signal Processing, ASSP-37, p. 1987-1990, December 1989; M. P. Fitz, “Further Results in the Fast Estimation of a Single Frequency”, IEEE Trans. Comm., COM-42, p. 862-864, March 1994 and M. Luise, R. Reggiannini, “Carrier Frequency Recovery in All-Digital Modems for Burst-Mode Transmission”, IEEE Trans. Comm., COM-43, p. 1169-1178, March 1995. The quoted methods certainly exhibit a relatively good efficiency in conjunction with acceptable complexity, but the extent to which they can be used is subject to substantial limitations. They can only be applied when the transmission system operates with phase modulation (phase shift keying, PSK) and, in addition, the transmission in the overall transmission system is free from inter symbol interference (ISI), that is to say the first Nyquist criterion is fulfilled.
In many practical applications, including the case of frequency-selective fading channels as, for example, in GSM mobile radio, freedom from inter-symbol interference still does not exist.